\begin{tikzpicture}[scale = \ScaleForProgressionFormulaFigs]
\tikzstyle{every node} = [font = \small]
	\foreach \x in {0}
	{
	\foreach \y in {-8}
		{
	
		\draw[black,thick,->] (\x-15,\y-2) -- (\x+15,\y-2);
		
			\foreach \t in {-14,-12,-10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10,12,14}
				{
					\fill (\t,\y-2) circle (.1);

				}
				\foreach \t in {-14,-10, -6, -2, 2, 6,10,14}
				{
					\fill (\t,\y-2) node[below]{$j$};

				}
				\foreach \t in {-12, -8, -4, 0, 4, 8,12}
				{
					\fill (\t,\y-2) node[below]{$i$};

				}	
				\foreach \t in {-13,-9, -5, -1, 3, 7, 11}
				{
					\draw[dashed] (\t,\y-2)--(\t, \y+8);

				}
			
				\fill (+13,\y+8.2) node[]{$Reg_{k-1}$};
				\fill (+9,\y+8.2) node[]{$\cdots$};
				\fill (+5,\y+8.2) node[]{$Reg_{4}$};
				\fill (+1,\y+8.2) node[]{$Reg_{3}$};
				\fill (-3,\y+8.2) node[]{$Reg_{2}$};
				\fill (-7,\y+8.2) node[]{$Reg_{1}$};
				\fill (-11,\y+8.2) node[]{$Reg_{0}$};
			

%				%working on the bracelets going bottom to top
				\draw[very thick]  plot[rounded corners] coordinates {(-14,\y+2)(-12,\y+1.5)(-12,\y+7.5)(12,\y+1.5)(12,\y+7.5)(14,\y+7)};
				\draw  plot[rounded corners] coordinates {(-14,\y+3)(-8,\y+1.5)(-8,\y+7.5)(14,\y+2)};
				\draw  plot[rounded corners] coordinates {(-14,\y+4)(-4,\y+1.5)(-4,\y+7.5)(14,\y+3)};
				\draw  plot[rounded corners] coordinates {(-14,\y+5)(0,\y+1.5)(0,\y+7.5)(14,\y+4)};
				\draw  plot[rounded corners] coordinates {(-14,\y+6)(4,\y+1.5)(4,\y+7.5)(14,\y+5)};
				\draw  plot[rounded corners] coordinates {(-14,\y+7)(8,\y+1.5)(8,\y+7.5)(14,\y+6)};
				

%				%working on marked point $j$ to $j$ going from left to right
				\draw  plot[rounded corners] coordinates {(-14,\y-1)(-10,\y-2)};
				\draw  plot[rounded corners] coordinates {(-14,\y-0)(-6,\y-2)};
				\draw  plot[rounded corners] coordinates {(-14,\y+1)(-2,\y-2)};
				
				
				\draw[very thick]  plot[rounded corners] coordinates {(-12,\y-2)(-12, \y+1.5)(2,\y-2)};
				\draw  plot[rounded corners] coordinates {(-8,\y-2)(-8, \y+1.5)(6,\y-2)};
				\draw  plot[rounded corners] coordinates {(-4,\y-2)(-4, \y+1.5)(10,\y-2)};
				\draw  plot[rounded corners] coordinates {(0,\y-2)(0, \y+1.5)(14,\y-2)};
				\draw  plot[rounded corners] coordinates {(4,\y-2)(4, \y+1.5)(14,\y-1)};
				\draw  plot[rounded corners] coordinates {(8,\y-2)(8, \y+1.5)(14,\y-0)};
				\draw  plot[rounded corners] coordinates {(12,\y-2)(12, \y+1.5)(14,\y+1)};

				
				
\draw[red] (-12,\y+1.5) circle (.3);
\draw[red] (-11.9,\y+1.6) node[right] {$c_0$};
}
}
\end{tikzpicture}
